Renormalization procedure for random tensor networks and the canonical tensor model
High Energy Physics - Theory
2015-04-15 v2 Statistical Mechanics
General Relativity and Quantum Cosmology
Abstract
We discuss a renormalization procedure for random tensor networks, and show that the corresponding renormalization-group flow is given by the Hamiltonian vector flow of the canonical tensor model, which is a discretized model of quantum gravity. The result is the generalization of the previous one concerning the relation between the Ising model on random networks and the canonical tensor model with N=2. We also prove a general theorem which relates discontinuity of the renormalization-group flow and the phase transitions of random tensor networks.
Cite
@article{arxiv.1501.05078,
title = {Renormalization procedure for random tensor networks and the canonical tensor model},
author = {Naoki Sasakura and Yuki Sato},
journal= {arXiv preprint arXiv:1501.05078},
year = {2015}
}
Comments
23 pages, 5 figures; Comments on first order transitions and discontinuity of RG added, and minor corrections